To our best knowledge, no convergence result is available for the Galerkin-type
approximations of the Dirichlet boundary control problems governed by the
parabolic equations with final observations. The fractional evolution equation
is an extension of the normal evolution equation, widely used to describe the
physical phenomena with memory effect [1]}. Recently, Harbir et
al. [2]} studied an optimal distributed control problem for a
space-time fractional diffusion equation. For the numerical analysis of the
optimal distributed problems governed by the time fractional diffusion
equations, we refer the reader to
[3]}, [4]}, [5]}, [6]}. To our knowledge,
no numerical analysis is available for the Dirichlet boundary control problems
governed by the fractional evolution equations. Hence, this paper tries to
analyze the Dirichlet boundary control problems for the fractional and normal
evolution equations in a unified way.
